1. Field of the Invention
The present invention relates to a device for controlling a running behavior of vehicles, and more particularly, to a device for conducting such a control of a four wheeled vehicle based upon a mathematical tire model simulating the performance of longitudinal and lateral forces vs. slip ratio of the tire of each wheel, with a compensation for a malfunction of a brake system.
2. Description of the Prior Art
It is known in the art that the tires of the wheels of vehicles such as automobiles generally exhibit a performance such as exemplarily shown in the map of FIG. 7 with respect to the relationship between the longitudinal or lateral force and the slip ratio. Of course, the actual performance of each particular tire differs from the shown performance in the shape of the curves as well as in the magnitude of the scales according to its tread pattern and respective operational conditions such as a road surface condition, etc.
Further, it is also known in the art that such a performance between the longitudinal or lateral force and the slip ratio of the tires of wheels of vehicles can be mathematically simulated by the following equations: ##EQU1##
wherein, generalizing by i such suffixes as fr, fl, rr and rl indicating the pertinency to front right, front left, rear right and rear left wheels of a common four wheeled vehicle each bearing the tire, Ftxi and Ftyi are the longitudinal and lateral components of a force Fti acting at a tire (wheel) as illustrated in FIG. 8, and 0 i is the angle between Fti and Ftxi, Si is a slip ratio of the tire defined as below by equation 5, and other parameters are as defined by the following: ##EQU2## PA1 wherein u is vehicle speed at the tire, R is radius of the tire, and .omega. is angular speed of the tire (-.infin.&lt;Si.ltoreq.1.0) ##EQU3## PA1 wherein .beta.i is slip angle of the wheel, Wi is vertical load on each wheel, Kb is the inclination at .beta.i=0 of a curve of the slip angle .beta.i vs. the lateral force Ftyi such as shown in FIG. 9 and Ks is the inclination at Si=0 of a curve of the slip angle Si vs. the longitudinal force Ftxi such as shown in FIG. 10. PA1 first means for cyclically calculating by a minute cycle period longitudinal force and lateral force of each of the at least either the front pair or the rear pair of the wheels in reference to slip ratio thereof according to a mathematical tire model of a relationship therebetween, so as to obtain a first longitudinal force and a first lateral force corresponding to a first slip ratio and a second longitudinal force and a second lateral force corresponding to zero slip ratio; PA1 second means for cyclically calculating by the minute cycle period longitudinal force, lateral force and yaw moment of the vehicle body based upon the longitudinal forces and the lateral forces of the at least either the front pair or the rear pair of the wheels, so as to obtain a first longitudinal force, a first lateral force and a first yaw moment of the vehicle body corresponding to the first longitudinal forces and the first lateral forces of the at least either the front pair or the rear pair of the wheels and a second longitudinal force, a second lateral force and a second yaw moment of the vehicle body corresponding to the second longitudinal forces and the second lateral forces of the at least either the front pair or the rear pair of the wheels; PA1 third means for cyclically modifying by the minute cycle period the second longitudinal force, the second lateral force and the second yaw moment of the vehicle body calculated by the second means with a longitudinal force, a lateral force and a yaw moment corresponding to an output of an outside running behavior controller, so as to obtain a nominal longitudinal force, a nominal lateral force and a nominal yaw moment, respectively; PA1 fourth means for cyclically calculating by the minute cycle period a difference between the nominal longitudinal force and the first longitudinal force, a difference between the nominal lateral force and the first lateral force and a difference between the nominal yaw moment and the first yaw moment; PA1 fifth means for cyclically calculating by the minute cycle period differentials of the longitudinal and lateral forces of each of the at least either the front pair or the rear pair of the wheels on the basis of the slip ratio thereof according to the mathematical tire model; PA1 sixth means for cyclically calculating by the minute cycle period differentials of the longitudinal force, lateral force and yaw moment of the vehicle body based upon differentials of the longitudinal and lateral forces of each of the at least either the front pair or the rear pair of the wheels on the basis of the slip ratio; PA1 seventh means for cyclically calculating by the minute cycle period a difference in the longitudinal force, a difference in the lateral force and a difference in the yaw moment of the vehicle body based upon the differentials thereof; PA1 eighth means for cyclically calculating by the minute cycle period a first difference between the difference in the longitudinal force calculated by the fourth means and the difference in the longitudinal force calculated by the seventh means, a second difference between the difference in the lateral force calculated by the fourth means and the differential-based difference in the lateral force calculated by the seventh means, and a third difference between the difference in the yaw moment calculated by the fourth means and the differential-based difference in the yaw moment calculated by the seventh means; PA1 ninth means for calculating by the minute cycle period differences in the slip ratio of each of the at least either the front pair or the rear pair of the wheels which minimize a weighted sum of squares of the first, second and third differences; and PA1 tenth means for selectively operating the brake means to change the slip ratio of each of the at least either the front pair or the rear pair of the wheels according to the difference thereof calculated by the ninth means. PA1 first means for cyclically calculating by a minute cycle period longitudinal force and lateral force of each of the front and rear pairs of wheels in reference to slip ratio thereof according to a mathematical tire model of a relationship therebetween, so as to obtain a first longitudinal force and a first lateral force corresponding to a first slip ratio and a second longitudinal force and a second lateral force corresponding to zero slip ratio; PA1 second means for cyclically calculating by the minute cycle period longitudinal force, lateral force and yaw moment of the vehicle body based upon the longitudinal forces and the lateral forces of the front pair and rear pairs of wheels, so as to obtain a first longitudinal force, a first lateral force and a first yaw moment of the vehicle body corresponding to the first longitudinal forces and the first lateral forces of the front and rear pairs of wheels and a second longitudinal force, a second lateral force and a second yaw moment of the vehicle body corresponding to the second longitudinal forces and the second lateral forces of the front and rear pairs of the wheels; PA1 third means for cyclically modifying by the minute cycle period the second longitudinal force, the second lateral force and the second yaw moment of the vehicle body calculated by the second means with a longitudinal force, a lateral force and a yaw moment corresponding to an output of an outside running behavior controller, so as to obtain a nominal longitudinal force, a nominal lateral force and a nominal yaw moment, respectively; PA1 fourth means for cyclically calculating by the minute cycle period a difference between the nominal longitudinal force and the first longitudinal force, a difference between the nominal lateral force and the first lateral force and a difference between the nominal yaw moment and the first yaw moment; PA1 fifth means for cyclically calculating by the minute cycle period differentials of the longitudinal and lateral forces of each of the front and rear pairs of wheels on the basis of the slip ratio thereof according to the mathematical tire model; PA1 sixth means for cyclically calculating by the minute cycle period differentials of the longitudinal force, lateral force and yaw moment of the vehicle body based upon differentials of the longitudinal and lateral forces of each of the front and rear pairs of wheels on the basis of the slip ratio; PA1 seventh means for cyclically calculating by the minute cycle period a difference in the longitudinal force, a difference in the lateral force and a difference in the yaw moment of the vehicle body based upon the differentials thereof; PA1 eighth means for cyclically calculating by the minute cycle period a first difference between the difference in the longitudinal force calculated by the fourth means and the difference in the longitudinal force calculated by the seventh means, a second difference between the difference in the lateral force calculated by the fourth means and the difference in the lateral force calculated by the seventh means, and a third difference between the difference in the yaw moment calculated by the fourth means and the difference in the yaw moment calculated by the seventh means; PA1 ninth means for calculating by the minute cycle period differences in the slip ratio of each of the front and rear pairs of wheels which minimize a weighted sum of squares of the first, second and third differences; and PA1 tenth means for selectively operating the brake means to change the slip ratio of each of the front and rear pairs of wheels according to the difference thereof calculated by the ninth means, PA1 wherein the third means further cyclically modify the nominal longitudinal force and the nominal yaw moment to be decreased as much as an additional longitudinal force and an additional yaw moment, respectively, the additional longitudinal force and the additional yaw moment corresponding respectively to a sum of a longitudinal force and a sum of a yaw moment generated in the vehicle by a difference between an uncontrollable braking force detected by the braking force detection means with respect to each of the front and rear pairs of wheels and a braking force to be applied thereto according to the change of the slip ratio thereof effected by the tenth means. PA1 eleventh means for cyclically calculating by the minute cycle period a weighted sum of a square of each of the differences in the slip ratio calculated by the ninth means; PA1 wherein the ninth means are modified to calculate the differences in the slip ratio so that a sum of the weighted sum calculated by the ninth means and the weighted sum calculated by the eleventh means is minimized. PA1 twelfth means for cyclically calculating by the minute cycle period a weighted sum of a square of each of respective sums of the slip ratio and the change thereof calculated by the ninth means; PA1 wherein the ninth means are modified to calculate the differences in the slip ratio so that a sum of the weighted sum calculated by the ninth means and the weighted sum calculated by the twelfth means is minimized.
The above equations are mathematical analyses of the relationships among such parameters as the longitudinal and lateral forces, the slip ratio, the slip angle, the vertical load and the friction coefficient with respect to each single tire. On the other hand, the running behavior of a four wheeled vehicles is a matter of interrelations among such respective performances of the four wheels. FIG. 11 shows an example of the yaw moment applied to the vehicle body of a four wheeled vehicle by a braking of each of the four wheels when the vehicle is running out of a straight course.
It would be contemplated to apply the above mathematical analyses to the running behavior control of four wheeled vehicles by preparing certain maps of relationships between or among each two or three of those parameters. However, if a four wheeled vehicle is mathematically controlled of its running behavior based upon a mathematical tire model such as expressed by the above-mentioned equations 1-9, since at least 11 parameters will be incorporated in the mathematical control calculations even when only one of the front and rear pairs of the wheels are controlled about their braking, only a very rough discrete points simulation would be available even by using the most modern microcomputers employable for an automobile running behavior control from the view point of the convenience of construction and economy.
In view of such an estrangement between the self-closed mathematical analyses applicable only to the performance of a single tire and the complicated interrelations of the performances of the pairs of front and rear wheels in the actual running behavior controls of four wheeled vehicles, our colleagues have proposed in a co-pending U.S. patent application Ser. No. 09/282,416 filed by the same assignee as the present assignee to provide a device for controlling a running behavior of four wheeled vehicles which can utilize a self-closed mathematical performance analysis of a single wheel tire such as described above effectively for a running behavior control of four wheeled vehicles even by using a microcomputer of a limited capacity.
According to the prior proposition, the device for controlling a running behavior of a vehicle based upon a force-slip performance of a tire, the vehicle having a vehicle body, a pair of front wheels and a pair of rear wheels, and brake means for selectively applying a controlled braking force to at least either the front pair or the rear pair of the wheels bearing the tires, comprises:
By the device of the above-mentioned construction, it is possible to execute a running behavior control of a four wheeled vehicle through mathematical control calculations based upon a mathematical tire model defining a relationship between longitudinal and lateral forces vs. slip ratio of each wheel such that the desired running behavior control of the vehicle is effectively accomplished with a minimum slip of at least a pair of front wheels or a pair of rear wheels to which a controlled braking is applied.
Since the running behavior control by the device according to the prior proposition is executed based upon a standard mathematical tire model, the control operation is continually effective even when the vehicle is running in such an operation range where the running behavior of the vehicle is so stabilized that some conventional running stability control devices adapted to be triggered by a certain parameter trespassing a threshold value do not yet operate.
On the other hand, in the modern electrically controlled brake systems such as those, for example, shown in co-pending U.S. patent application Ser. No. 09/365,222, there is a probability, improbable in the conventional hydraulic brake systems, that the brake of one of the wheels erroneously operates such that a braking force is uncontrollably applied to the wheel due to the incorporation of the solenoid valves. When this happens, the running course of the vehicle will be much affected unless the driver is highly skilled in the driving.